Efficient binary tomographic reconstruction

TL;DR

This paper introduces a fast, heuristic algorithm for binary tomographic reconstruction from limited projections, utilizing a nonlinear transformation to achieve exact pixel recovery efficiently.

Contribution

A novel heuristic method using a nonlinear transformation for efficient binary tomographic reconstruction from few projections.

Findings

Achieves exact binary image reconstruction from limited projections.

Reconstructs images up to 1 million pixels in a few seconds.

Outperforms previous methods in efficiency and computation time.

Abstract

Tomographic reconstruction of a binary image from few projections is considered. A novel {\em heuristic} algorithm is proposed, the central element of which is a nonlinear transformation $\psi(p)=\log(p/(1-p))$ of the probability $p$ that a pixel of the sought image be 1-valued. It consists of backprojections based on $\psi(p)$ and iterative corrections. Application of this algorithm to a series of artificial test cases leads to exact binary reconstructions, (i.e recovery of the binary image for each single pixel) from the knowledge of projection data over a few directions. Images up to $10^6$ pixels are reconstructed in a few seconds. A series of test cases is performed for comparison with previous methods, showing a better efficiency and reduced computation times.